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51.
The main aspect of the paper consists in the application of a particular theorem of separation between two sets to the image
associated with a constrained extremum problem. In the image space, the two sets are a convex cone, which depends on the constraints
(equalities or inequalities) of the given problem, and its image. In this way, a condition for the existence of a regular
saddle point (i.e., a sufficient optimality condition) is obtained. This regularity condition is compared with those existing
in the literature. 相似文献
52.
Beatriz Hernández-Jiménez Rafaela Osuna-Gómez 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2463-2475
For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective non-regular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions. 相似文献
53.
The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided. 相似文献
54.
In this paper, we develop effective methods for solving the power-networking problem encountered by the Tulsa Metro Chamber. The primary objective is the maximization of unique contacts made in meetings with multiple rotations of participants. Mixed-integer and constraint-programming models are developed to optimize small- to medium-scale problems, and a heuristic method is developed for large-scale problems representative of the Chamber’s application. Tight bounds on the dual objective are presented. The constraint-programming model developed as phase one for the heuristic yields many new best-known solutions to the related social-golfer problem. The solutions generated for the power-networking problem enables the Chamber of Commerce to plan meeting assignments much more effectively. 相似文献
55.
The capability of nonlinear analysis methods in tracing the equilibrium path depends on how to return to static status. In this paper, some residual factors existed in the iteration steps are employed. By setting the residual load parameter to zero, minimizing its factor and the residual displacement parameter, three novel constraint equations are obtained. The new formulas are proved by numerical examples. All obtained results illustrate the minimum residual load scheme's robustness in comparison with the cylindrical arc-length algorithm and other previous strategies. Moreover, the capacities of new procedures in tracing the load and displacement limit points are assessed. 相似文献
56.
The “dual constraint” model developed by Mead, Van Dyke et al. is here extended by inclusion of “early-time” contour-length
fluctuations and constraint-release Rouse relaxation, and then evaluated by comparing its predictions with literature data
for over 50 different linear and star polymers. By combining the reptation model of Doi and Edwards with contour-length fluctuations
and constraint release, the model provides a systematic approach to prediction of the rheological properties of polymers.
The parameters are taken from the literature and used consistently for linear polymers, star polymers, and their mixtures
having the same chemical compositions. In most cases, the predictions of the model appears to agree well with data for monodisperse,
bidisperse, and polydisperse linear and star polymers, except at low molecular weights.
Received: 23 December 1999 Accepted: 28 March 2000 相似文献
57.
Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions 总被引:1,自引:0,他引:1
The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions
is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests
of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to
cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with
the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion
to show that this variation can be interpreted using the critical stress intensity factorK
Cand a second parameterT orA
3,whereT andA
3are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this
constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release
rateG
Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving
or instability under mode I loading conditions. Experimental data are presented and compared with the theory. 相似文献
58.
Oliver Stein 《计算数学(英文版)》2006,24(6):719-732
We study the smoothing method for the solution of generalized semi-infinite optimiza-tion problems from(O.Stein,G.Still:Solving semi-infinite optimization problems withinterior point techniques,SIAM J.Control Optim.,42(2003),pp.769-788).It is shownthat Karush-Kuhn-Tucker points of the smoothed problems do not necessarily converge toa Karush-Kuhn-Tucker point of the original problem,as could be expected from resultsin(F.Facchinei,H.Jiang,L.Qi:A smoothing method for mathematical programs withequilibrium constraints,Math.Program.,85(1999),pp.107-134).Instead, they mightmerely converge to a Fritz John point.We give,however,different additional assumptionswhich guarantee convergence to Karush-Kuhn-Tucker points. 相似文献
59.
This paper studies noncompact feasible sets of a semi-infinite optimization problem which are defined by finitely many equality constraints and infinitely many inequality constraints. The main result is the equivalence of the overall validity of the Extended Mangasarian Fromovitz Constraint Qualification with certain (topological) stability conditions. Furthermore, two perturbation theorems being of independent interest are presented.This work was supported by the Deutsche Forschungsgemeinschaft under grant Gu 304/1-2. 相似文献
60.
Universal duality in conic convex optimization 总被引:1,自引:0,他引:1
Given a primal-dual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended
real line, then the duality gap is zero, unless both problems are infeasible, in which case the optimal values are +∞ and
−∞. In contrast, for optimization problems over nonpolyhedral convex cones, a nonzero duality gap can exist when either the
primal or the dual is feasible.
For a pair of dual conic convex programs, we provide simple conditions on the ``constraint matrices' and cone under which
the duality gap is zero for every choice of linear objective function and constraint right-hand side. We refer to this property as ``universal duality'. Our
conditions possess the following properties: (i) they are necessary and sufficient, in the sense that if (and only if) they
do not hold, the duality gap is nonzero for some linear objective function and constraint right-hand side; (ii) they are metrically
and topologically generic; and (iii) they can be verified by solving a single conic convex program. We relate to universal
duality the fact that the feasible sets of a primal convex program and its dual cannot both be bounded, unless they are both
empty. Finally we illustrate our theory on a class of semidefinite programs that appear in control theory applications.
This work was supported by a fellowship at the University of Maryland, in addition to NSF grants DEMO-9813057, DMI0422931,
CUR0204084, and DoE grant DEFG0204ER25655. Any opinions, findings, and conclusions or recommendations expressed in this paper
are those of the authors and do not necessarily reflect the views of the National Science Foundation or those of the US Department
of Energy. 相似文献